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Heat conduction by photons through superconducting leads

Heat conduction by photons through superconducting leads. W.Guichard Université Joseph Fourier and Institut Neel, Grenoble, France. M. Meschke, and J.P. Pekola Low Temperature Laboratory, Helsinki University of Technology, Espoo, Finland. Thermal conductance. T 2. T 1. Heat flow.

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Heat conduction by photons through superconducting leads

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  1. Heat conduction by photons through superconducting leads W.Guichard Université Joseph Fourier and Institut Neel, Grenoble, France M. Meschke, and J.P. Pekola Low Temperature Laboratory, Helsinki University of Technology, Espoo, Finland

  2. Thermal conductance T2 T1 Heat flow Thermal conductance Heat flow (T1 > T2) What conducts heat in a solid ? Electrons (important for metals) Phonons (lattice vibrations) Q T T +T Quantum of thermal conductance and what about photons ?

  3. Measurement of quantized thermal conductance Quantized electronic thermal conductance 2DEG in a GaAs-AlGaAs heterostructure Molenkamp et al. Phys. Rev. Lett 68 (1992) Quantized phonon thermal conductance Silicon nitride membrane K. Schwab et al. , Nature 404 (2000)

  4. Energy relaxation in a submicron metal island Pex In thermal equilibrium: Electron-electron collissions Electron-phonon collisions Pep M.Meschke et al.

  5. Energy relaxation in a submicron metal island Pex Pe In thermal equilibrium: Electron-electron collisions Electron-phonon collisions Pep +Electron-photon „radiative“ relaxation ? M.Meschke et al.

  6. Heat transported between two resistors Ge= ? Voltage noise emitted by resistor Ri: 1D Black body radiation R1,T1 R2,T2 Net heat flow from hot to cold resistor: Quantum of thermal Conductance: Schmidt et al.,Phys. Rev. Lett., 93 (2004)

  7. Competition between ep- and e- coupling Cross-over temperature: TCO

  8. Typical experimental set-up Island size: 6.6 mm x 0.8 mm x 20 nm SQUID junction size: 3 mm x 0.1 mm SINIS junction size: 3 mm x 0.1 mm Electrical circuit Ib Iheat V

  9. Actual experimental configuration: tunable impedance between the resistors

  10. Electrical Model I L0 L0 L0 Transmission line: C0 C0 C0 Here: R2 R1 L0 L0 L0 C0 C0 C0 L~30 μm Tunable inductance: R2 R1

  11. Electrical Model II CSQUID=30fF LSQ CSQ R2 R1 LSQ CSQ

  12. Thermal model Typical parameter values: P1 = 1 fW P2 = 0

  13. SINIS thermometer Probes electron temperature of N island (and not of S!) in the case of T/Tc<0.4 Low leakage of junctions

  14. Measured variation of island temperature:

  15. Measured variation of island temperature:variation of bath temperature Flux Φ0 Ic=20nA CSQUID=15fF R1=R2=200 P1=1fW P2=0

  16. Increase island temperature Te1 T0=150mK T0<40mK Flux Φ0 Flux Φ0

  17. Measured variation of island temperature:amplitude of modulation

  18. Conclusion • -First observation of the crossover from phonon relaxation to radiative photon relaxation at temperatures of about 100 mK • Thermal and electrical model explain quite well the measured data • Implications on: • performance of bolometers (sensitivity): coupling to the heat bath • removing excessive heat from devices at milli-kelvin range

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